Science (English Medium) Class 12 - CBSE Question Bank Solutions

If the area of a circle increases at a uniform rate, then prove that perimeter varies inversely as the radius

A kite is moving horizontally at a height of 151.5 meters. If the speed of kite is 10 m/s, how fast is the string being let out; when the kite is 250 m away from the boy who is flying the kite? The height of boy is 1.5 m.

Two men A and B start with velocities v at the same time from the junction of two roads inclined at 45° to each other. If they travel by different roads, find the rate at which they are being seperated.

A man, 2m tall, walks at the rate of `1 2/3` m/s towards a street light which is `5 1/3`m above the ground. At what rate is the tip of his shadow moving? At what rate is the length of the shadow changing when he is `3 1/3`m from the base of the light?

A swimming pool is to be drained for cleaning. If L represents the number of litres of water in the pool t seconds after the pool has been plugged off to drain and L = 200 (10 – t)². How fast is the water running out at the end of 5 seconds? What is the average rate at which the water flows out during the first 5 seconds?

The volume of a cube increases at a constant rate. Prove that the increase in its surface area varies inversely as the length of the side

x and y are the sides of two squares such that y = x – x². Find the rate of change of the area of second square with respect to the area of first square.

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when side is 10 cm is ______.

A ladder, 5 meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is ______.

Let A = { 2, 3, 6 } Which of the following relations on A are reflexive?

Let R be the relation on N defined as by x + 2 y = 8 The domain of R is ____________.

Which of the following is not an equivalence relation on I, the set of integers: x, y

R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)} be a relation on A, then R is ____________.

Let A = {1, 2, 3}. Which of the following is not an equivalence relation on A?

Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ____________.

Let A = {1, 2, 3}, then the relation R = {(1, 1), (1, 2), (2, 1)} on A is ____________.

If A is a finite set containing n distinct elements, then the number of relations on A is equal to ____________.

Let A = {1, 2, 3}, then the domain of the relation R = {(1, 1), (2, 3), (2, 1)} defined on A is ____________.

Let A = {1, 2, 3, 4, 5, 6} Which of the following partitions of A correspond to an equivalence relation on A?

A relation R on a non – empty set A is an equivalence relation if it is ____________.